Abstract
The fitted mesh numerical method is presented to solve parabolic problems involving an interior layer. A uniform mesh was applied in the temporal direction and fitted mesh type on the space variable yields the discrete problem. The convergence of the method is established and shown to the second-order in the temporal direction with the first-order convergent in the spatial one. Further, the scheme is proven to be parameter independent convergent and also confirmed by numerical experiments. In a nutshell, novelty of the present scheme is uniformly convergent and gives a more accurate solution than some existing methods in the literature.
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